# Uncertainty measures: The big picture

arXiv: https://arxiv.org/abs/2104.06839 · HTML: https://mlsanity.com/paper/2104.06839/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 183 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 8 of 8)

- [Visions of a generalized probability theory](https://mlsanity.com/paper/1810.10341/) (2018)
- [Decision under Uncertainty](https://mlsanity.com/paper/1304.1527/) (2013)
- [The Dynamic of Belief in the Transferable Belief Model and Specialization-Generalization Matrices](https://mlsanity.com/paper/1303.5408/) (2013)
- [A New Approach to Updating Beliefs](https://mlsanity.com/paper/1304.1119/) (2013)
- [Generalizing the Dempster-Shafer Theory to Fuzzy Sets](https://mlsanity.com/paper/1304.2383/) (2013)
- [Higher Order Probabilities](https://mlsanity.com/paper/1304.2714/) (2013)
- [Metaprobability and Dempster-Shafer in Evidential Reasoning](https://mlsanity.com/paper/1304.3427/) (2013)
- [Evidential Confirmation as Transformed Probability](https://mlsanity.com/paper/1304.3439/) (2013)

## Built on by (most cited first, 8 of 8)

- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Reasoning with random sets: An agenda for the future](https://mlsanity.com/paper/2401.09435/) (2023)
- [Epistemic Wrapping for Uncertainty Quantification](https://mlsanity.com/paper/2505.02277/) (2025)
- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Statistical inference with belief functions: A survey](https://mlsanity.com/paper/2605.07908/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)

## Abstract (arXiv)

Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty have been proposed, many of them generalisations of classical probability. As we show here, such frameworks can be organised into clusters sharing a common rationale, exhibit complex links, and are characterised by different levels of generality. Our goal is a critical appraisal of the current landscape in uncertainty theory.